Question

Solve the pair of equations 3/x-1/y=-9 and 2/x+3/y=5

Answer 1

Answer

• x = - 1/2 , y = 1/3

Given

$\bullet \;\; \tt \dfrac{3}{x}-\dfrac{1}{y}=-9\\\\\bullet \;\; \tt \dfrac{2}{x}+\dfrac{3}{y}=5$

To Find

• x and y values

Solution

$\tt \dfrac{3}{x}-\dfrac{1}{y}=-9\\\\\tt \implies \dfrac{9}{x}-\dfrac{3}{y}=-27...(1)[Multiply\ with\ 3]\\\\\tt \dfrac{2}{x}+\dfrac{3}{y}=5...(2)$

By adding (1) , (2) , we get ,

$\implies \tt \bigg(\dfrac{9}{x}-\dfrac{3}{y}\bigg)+\bigg(\dfrac{2}{x}+\dfrac{3}{y}\bigg)=-27+5\\\\\implies \tt \dfrac{9}{x}-\cancel{\dfrac{3}{y}}+\dfrac{2}{x}+\cancel{\dfrac{3}{y}}=-22\\\\\implies \tt \dfrac{11}{x}=-22\\\\\implies \tt x=\dfrac{11}{-22}\\\\\implies \tt x=- \dfrac{1}{2}$

Sub. x value in (2) , we get ,

$\implies \tt \dfrac{2}{(-1/2)}+\dfrac{3}{y}=5\\\\\implies \tt -4+\dfrac{3}{y}=5\\\\\implies \tt \dfrac{3}{y}=9\\\\\implies \tt y=\dfrac{3}{9}\\\\\implies \tt y=\dfrac{1}{3}$